Exponential Distribution

Modeling the time until an event occurs in a Poisson process.

The "Time Between Events" Distribution

The Exponential distribution is a continuous probability distribution that models the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.

It is the continuous analogue of the Geometric distribution. While the Geometric distribution models the number of trials until the first success, the Exponential distribution models the amount of time until the next event. In finance, it's used to model the time between trades, the time until a bond defaults, or the duration until a stock price hits a certain level.

The Formula
The probability density function (PDF) is given by:
f(x;λ)=λe−λxf(x; \lambda) = \lambda e^{-\lambda x}
  • x≥0x \ge 0 is the time variable.
  • λ>0\lambda > 0 (lambda) is the rate parameter, the average number of events per unit of time.
Interactive Exponential Distribution
Adjust the rate parameter (λ) to see how the shape of the distribution changes. A higher rate means events happen more frequently, so the probability of a short waiting time is high.